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# Is p > q? (1) p/q > 1 (2) (p - q)/q > (p - q)/p

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Intern
Joined: 06 Feb 2018
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Location: India
Is p > q? (1) p/q > 1 (2) (p - q)/q > (p - q)/p  [#permalink]

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01 Mar 2018, 14:25
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Difficulty:

75% (hard)

Question Stats:

51% (02:12) correct 49% (01:47) wrong based on 67 sessions

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Is p > q?

(1) $$\frac{p}{q} > 1$$

(2) $$\frac{(p-q)}{q} > \frac{(p-q)}{p}$$
Retired Moderator
Joined: 25 Feb 2013
Posts: 1196
Location: India
GPA: 3.82
Re: Is p > q? (1) p/q > 1 (2) (p - q)/q > (p - q)/p  [#permalink]

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01 Mar 2018, 20:23
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raashiedm wrote:
Is p>q?

(1) $$\frac{p}{q} > 1$$
(2) $$\frac{(p-q)}{q} > \frac{(p-q)}{p}$$

Statement 1: Both $$p$$ & $$q$$ are either positive or negative. if $$p=2$$ & $$q=1$$, then we have $$p>q$$ & $$\frac{p}{q}>1$$, but if $$p=-2$$ & $$q=-1$$, then $$\frac{p}{q}>1$$ but $$p<q$$. Hence Insufficient

Statement 2: $$\frac{p-q}{q}-\frac{p-q}{p}>0 =>\frac{(p-q)^2}{pq}>0$$

Now $$(p-q)^2>0$$, hence $$pq>0$$. This implies both $$p$$ & $$q$$ are either positive or negative. Same as Statement 1. Insufficient

Combining 1 & 2: We know either $$p$$ & $$q$$ are positive or negative but we cannot determine the value of $$p$$ & $$q$$. Hence Insufficient

Option E
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Re: Is p > q? (1) p/q > 1 (2) (p - q)/q > (p - q)/p  [#permalink]

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03 Mar 2018, 02:26
raashiedm wrote:
Is p>q?

(1) $$\frac{p}{q} > 1$$
(2) $$\frac{(p-q)}{q} > \frac{(p-q)}{p}$$

Easy E.

Plug in the numbers -3 and -2 for both the statements. Both statements together are not sufficient to answer the question.
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Re: Is p > q? (1) p/q > 1 (2) (p - q)/q > (p - q)/p  [#permalink]

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08 Mar 2018, 03:07
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Re: Is p > q? (1) p/q > 1 (2) (p - q)/q > (p - q)/p  [#permalink]

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08 Mar 2018, 08:08
raashiedm wrote:
Is p > q?

(1) $$\frac{p}{q} > 1$$

(2) $$\frac{(p-q)}{q} > \frac{(p-q)}{p}$$

Neither of the statements gives us any information about the sign of p and q. Both the statements are insufficient to answer.

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Re: Is p > q? (1) p/q > 1 (2) (p - q)/q > (p - q)/p  [#permalink]

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24 Apr 2019, 11:12

As per statement 1 : p>0 and q>0 or p<0 and q<0
Not sufficient

As per statement 2 : same as above

As per both the statements : same as above

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Re: Is p > q? (1) p/q > 1 (2) (p - q)/q > (p - q)/p   [#permalink] 24 Apr 2019, 11:12
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